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The dynamics of a Leslie-Gower type tritrophic model are analyzed. The model considers the interaction among three populations, a resource, a predator and a superpredator. It is assumed that the predator is generalist and its interaction with the resource is according to a general Holling-type functional response. Furthermore, it is assumed that the superpredator is specialist and its interaction with the predator follows a Holling type II functional response. The goal of this work is to show conditions that guarantee the coexistence of the three species. To do this, the existence of a stable equilibrium point or a stable limit cycle is demonstrated, which appears via a bifurcation. In addition, the analytical results are exemplified through numerical simulations.

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Chronic Myeloid Leukemia is a blood cancer for which standard therapy with Tyrosine-Kinase Inhibitors is successful in the majority of patients. After discontinuation of treatment half of the well-responding patients either present undetectable levels of tumor cells for a long time or exhibit sustained fluctuations of tumor load oscillating at very low levels. Motivated by the consequent question of whether the observed kinetics reflect periodic oscillations emerging from tumor-immune interactions, in this work, we analyze a system of ordinary differential equations describing the immune response to CML where both the functional response against leukemia and the immune recruitment exhibit optimal activation windows. Besides investigating the stability of the equilibrium points, we provide rigorous proofs that the model exhibits at least two types of bifurcations: a transcritical bifurcation around the tumor-free equilibrium point and a Hopf bifurcation around a biologically plausible equilibrium point, providing an affirmative answer to our initial question. Focusing our attention on the Hopf bifurcation, we examine the emergence of limit cycles and analyze their stability through the calculation of Lyapunov coefficients. Then we illustrate our theoretical results with numerical simulations based on clinically relevant parameters. Besides the mathematical interest, our results suggest that the fluctuating levels of low tumor load observed in CML patients may be a consequence of periodic orbits arising from predator-prey-like interactions.

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We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R∗>1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R∗<1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R∗ appearing in this model are both responsible for the existence of endemic states.

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We developed a mathematical model to simulate dynamics associated with the proliferation of Geobacter and ultimately optimize cellular operation by analyzing the interaction of its components. The model comprises two segments: an initial part comprising a logistic form and a subsequent segment that incorporates acetate oxidation as a saturation term for the microbial nutrient medium. Given that four parameters can be obtained by minimizing the square root of the mean square error between experimental Geobacter growth and the mathematical model, the model underscores the importance of incorporating nonlinear terms. The determined parameter values closely align with experimental data, providing insights into the mechanisms that govern Geobacter proliferation. Furthermore, the model has been transformed into a scaleless equation with only two parameters to simplify the exploration of qualitative properties. This allowed us to conduct stability analysis of the fixed point and construct a co-dimension two bifurcation diagram.

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This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model's parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures.

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Chikungunya is a vector-borne viral disease transmitted by Aedes aegypti and Aedes albopictus mosquitoes. It does not have any specific treatment, and there is no vaccine. Recent epidemiological data have indicated that a relapse of the infection can occur within three months of the initial infection; however, until now, mathematical models for the spread of the disease have not considered this factor. We propose a mathematical model for the transmission of the Chikungunya virus that considers relapse. We calculated the basic reproductive number $ (R_0) $ of the disease by using the next-generation operator method. We proved the existence of a forward bifurcation. We determined the existence and the global stability of the equilibrium points by using the Lyapunov function method. We fitted the model to data from an outbreak in 2015 in Acapulco, Mexico to estimate the model parameters and $ R_0 $ with the Bayesian approach via a Hamiltonian Monte Carlo method. In the local sensitivity analysis, we found that the fraction of infected individuals who become asymptomatic has a strong impact on the basic reproductive number and makes some control measures insufficient. The impact of the fraction of infected individuals who become asymptomatic should be considered in Chikungunya control strategies.

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Coffee is a relevant agricultural product in the global economy, with the amount and quality of the bean being seriously affected by the coffee berry borer Hypothenemus hampei (Ferrari), CBB, its principal pest. One of the ways to deal with this beetle is through biological control agents, like ants (Hymenoptera: Formicidae), some of which are characterized by naturally inhabiting coffee plantations and feeding on CBB in all their life stages. Our paper considers a predator-prey interaction between these two insects through a novel mathematical model based on ordinary differential equations, where the state variables correspond to adult CBBs, immature CBBs, and ants from one species, without specifying whether preying on the CBB is among their feeding habits, in both adult and immature stages. Through this new mathematical model, we could qualitatively predict the different dynamics present in the system as some meaningful parameters were varied, filling the existing gap in the literature and envisioning ways to manage pests. Mathematically, the system's equilibrium points were determined, and its stability was studied through qualitative theory. Bifurcation theory and numerical simulations were applied to illustrate the stability of the results, which were interpreted as conditions of the coexistence of the species, as well as conditions for eradicating the pest, at least theoretically, through biocontrol action in combination with other actions focused on eliminating only adult CBBs.

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Throughout the progress of epidemic scenarios, individuals in different health classes are expected to have different average daily contact behavior. This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better. Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation. Therefore, we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses. Our incidence rate function is formulated, taking inspiration from recent adaptive algorithms. It incorporates contact behavior for individuals in each health class. We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios. The relationship between the different contact rates heavily influences these conditions. Numerical examples highlight the effect of temporarily recovered individuals and initial conditions on infected population persistence.

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Large variability exists across brain regions in health and disease, considering their cellular and molecular composition, connectivity, and function. Large-scale whole-brain models comprising coupled brain regions provide insights into the underlying dynamics that shape complex patterns of spontaneous brain activity. In particular, biophysically grounded mean-field whole-brain models in the asynchronous regime were used to demonstrate the dynamical consequences of including regional variability. Nevertheless, the role of heterogeneities when brain dynamics are supported by synchronous oscillating state, which is a ubiquitous phenomenon in brain, remains poorly understood. Here, we implemented two models capable of presenting oscillatory behavior with different levels of abstraction: a phenomenological Stuart-Landau model and an exact mean-field model. The fit of these models informed by structural- to functional-weighted MRI signal (T1w/T2w) allowed us to explore the implication of the inclusion of heterogeneities for modeling resting-state fMRI recordings from healthy participants. We found that disease-specific regional functional heterogeneity imposed dynamical consequences within the oscillatory regime in fMRI recordings from neurodegeneration with specific impacts on brain atrophy/structure (Alzheimer's patients). Overall, we found that models with oscillations perform better when structural and functional regional heterogeneities are considered, showing that phenomenological and biophysical models behave similarly at the brink of the Hopf bifurcation.

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Let the individuals of a population be divided into two groups with different personal habits. The core group is associated with health risk behaviors; the non-core group avoids unhealthy activities. Assume that the infected individuals of the core group can spread a contagious disease to the whole population. Also, assume that cure does not confer immunity. Here, an epidemiological model written as a set of ordinary differential equations is proposed to investigate the infection propagation in this population. In the model, migrations between these two groups are allowed; however, the transitions from the non-core group into the core group prevail. These migrations can be either spontaneous or stimulated by social pressure. It is analytically shown that, in the scenario of spontaneous migration, the disease is either naturally eradicated or chronically persists at a constant level. In the scenario of stimulated migration, in addition to eradication and constant persistence, self-sustained oscillations in the number of sick individuals can also be found. These analytical results are illustrated by numerical simulations and discussed from a public health perspective.

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Covid-19, caused by severe acute respiratory syndrome coronavirus 2, broke out as a pandemic during the beginning of 2020. The rapid spread of the disease prompted an unprecedented global response involving academic institutions, regulatory agencies, and industries. Vaccination and nonpharmaceutical interventions including social distancing have proven to be the most effective strategies to combat the pandemic. In this context, it is crucial to understand the dynamic behavior of the Covid-19 spread together with possible vaccination strategies. In this study, a susceptible-infected-removed-sick model with vaccination (SIRSi-vaccine) was proposed, accounting for the unreported yet infectious. The model considered the possibility of temporary immunity following infection or vaccination. Both situations contribute toward the spread of diseases. The transcritical bifurcation diagram of alternating and mutually exclusive stabilities for both disease-free and endemic equilibria were determined in the parameter space of vaccination rate and isolation index. The existing equilibrium conditions for both points were determined in terms of the epidemiological parameters of the model. The bifurcation diagram allowed us to estimate the maximum number of confirmed cases expected for each set of parameters. The model was fitted with data from São Paulo, the state capital of SP, Brazil, which describes the number of confirmed infected cases and the isolation index for the considered data window. Furthermore, simulation results demonstrate the possibility of periodic undamped oscillatory behavior of the susceptible population and the number of confirmed cases forced by the periodic small-amplitude oscillations in the isolation index. The main contributions of the proposed model are as follows: A minimum effort was required when vaccination was combined with social isolation, while additionally ensuring the existence of equilibrium points. The model could provide valuable information for policymakers, helping define disease prevention mitigation strategies that combine vaccination and non-pharmaceutical interventions, such as social distancing and the use of masks. In addition, the SIRSi-vaccine model facilitated the qualitative assessment of information regarding the unreported infected yet infectious cases, while considering temporary immunity, vaccination, and social isolation index.

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We constructed a Susceptible-Addicted-Reformed model and explored the dynamics of nonlinear relapse in the Reformed population. The transition from susceptible considered at-risk is modeled using a strictly decreasing general function, mimicking an influential factor that reduces the flow into the addicted class. The basic reproductive number is computed, which determines the local asymptotically stability of the addicted-free equilibrium. Conditions for a forward-backward bifurcation were established using the basic reproductive number and other threshold quantities. A stochastic version of the model is presented, and some numerical examples are shown. Results showed that the influence of the temporarily reformed individuals is highly sensitive to the initial addicted population.

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The literature has reported the isolation of arsenate-dependent growing microorganisms which lack a canonical homolog for respiratory arsenate reductase, ArrAB. We recently isolated an arsenate-dependent growing bacterium from volcanic arsenic-bearing environments in Northern Chile, Fusibacter sp. strain 3D3 (Fas) and studied the arsenic metabolism in this Gram-positive isolate. Features of Fas deduced from genome analysis and comparative analysis with other arsenate-reducing microorganisms revealed the lack of ArrAB coding genes and the occurrence of two arsC genes encoding for putative cytoplasmic arsenate reductases named ArsC-1 and ArsC-2. Interestingly, ArsC-1 and ArsC-2 belong to the thioredoxin-coupled family (because of the redox-active disulfide protein used as reductant), but they conferred differential arsenate resistance to the E. coli WC3110 ΔarsC strain. PCR experiments confirmed the absence of arrAB genes and results obtained using uncouplers revealed that Fas growth is linked to the proton gradient. In addition, Fas harbors ferredoxin-NAD+ oxidoreductase (Rnf) and electron transfer flavoprotein (etf) coding genes. These are key molecular markers of a recently discovered flavin-based electron bifurcation mechanism involved in energy conservation, mainly in anaerobic metabolisms regulated by the cellular redox state and mostly associated with cytoplasmic enzyme complexes. At least three electron-bifurcating flavoenzyme complexes were evidenced in Fas, some of them shared in conserved genomic regions by other members of the Fusibacter genus. These physiological and genomic findings permit us to hypothesize the existence of an uncharacterized arsenate-dependent growth metabolism regulated by the cellular redox state in the Fusibacter genus.

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ABSTRACT: The following manuscript presents two paediatric cases with incidental finding of unilateral accessory mental foramina. Both the cases illustrate CBCT evaluation of a unilateral accessory foramina on the left side of the mandible, one of which, is a 12-year-old baby girl with pre-diagnosed medical history of precocious puberty and oral findings of supernumerary teeth and the other is an 8-year-old boy with oral bifurcation cyst. The not so frequent presence of additional foramina and canals in the mandible are frequently undervalued in clinical procedures and to our knowledge has not yet been reported in paediatric cases in the literature so far. In these case reports, authors attempt to document a rare and first of its type ever reported anatomic variant of mandible in paediatric patients in the whole literature.

RESUMEN: El manuscrito presenta dos casos pediátricos con hallazgo incidental de forámenes mentonianos accesorios unilaterales. Ambos casos se refieren a la evaluación CBCT de un foramen accesorio unilateral en el lado izquierdo de la mandíbula, uno de los cuales era una niña de 12 años con antecedentes medicos prediagnosticados de pubertad precoz y hallazgos orales de dientes supernumerarios y el otro un niño de 8 años con quiste de bifurcación bucal. La presencia no tan frecuente de forámenes y canales adicionales en la mandíbula se subestima con frecuencia en los procedimientos clínicos y, hasta donde sabemos, aún no se ha informado en casos pediátricos en la literatura hasta el momento. En esta serie de casos, los autores intentan documentar una variante anatómica rara y primera de su tipo de la mandíbula en pacientes pediátricos en toda la literatura.

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Serotonin, dopamine and norepinephrine are monoamine neurotransmitters that modulate our mood state. Hence, imbalances in the levels of these neurotransmitters have been linked to the incidence of several psychiatric disorders. Here, a mathematical model written in terms of ordinary differential equations is proposed to represent the interaction of these three neurotransmitters. It is analytically and numerically shown that this model can experience a Hopf bifurcation. Thus, by varying a parameter value, the neurotransmitter levels can change from a steady state to an oscillatory behavior, which may be at least a partial explanation of the mood swings observed in depressed people.

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We propose a modified mathematical model of the quasispecies type to analyze an unstable tumor progression evolution. In our study, we consider a heterogeneous population with different individuals, generated by the accumulation of successive mutations. Our model's main feature is that it allows for variable growth rates for each subpopulation and takes into account mutations from nonconsecutive types of mutants. Bifurcations and linear stability of the steady states are analyzed. We focus on two equilibria; one of them implies the coexistence of anomalous growth and genetically unstable cells. The other one yields the dominance of the anomalous growth population and the extinction of the malignant cells. However, linear stability analysis of the second equilibrium is inconclusive and suggests a suitable environment for the study of periodic therapy. This is carried out by introducing a small perturbation modeling the effect of a periodic medical treatment. As a result, a Zero-Hopf periodic orbit is identified, showing a cyclic behavior among the populations, with a strong dominance of the parental anomalous growth cell population.

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In this paper, we study a diffusive SIRS-type epidemic model with transfer from the infectious to the susceptible class. Our model includes a general nonlinear incidence rate and spatially heterogeneous diffusion coefficients. We compute the basic reproduction number R 0 of our model and establish the global stability of the disease-free steady state when R 0 < 1 . Furthermore, we study the uniform persistence when R 0 > 1 and perform a bifurcation analysis for a special case of our model. Some numerical simulations are presented to illustrate the dynamics of the solutions as the model parameters are varied.

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INTRODUCTION: Surgical approach of aortoiliac occlusive disease (AOD) with aorto-bi-femoral graft or endarterectomy, has been the first line treatment with patency rates up to 90%. Nevertheless, this procedure has an early mortality rate of 4%. Vascular complications of aorto-bi-femoral graft have an average incidence of 5-10% and development of incisional hernia in 10% of the cases. The Covered Endovascular Reconstruction of Aortic Bifurcation or CERAB technique, as a new approach is shaping up to be a promising approach. However, there are few studies in Latin America and the Caribbean. MATERIALS AND METHODS: Retrospective multicenter study. All patients treated with the CERAB technique between February 2015 and June 2021 in three hospitals. RESULTS: A total of 9 patients (5 male and 4 female) were treated with the CERAB technique. Only one patient died. Of the total number of patients, 41.2% had a TASC II - C classification, and 58.8% had a TASC II - D classification. Complications included dissection in only 2 patients, massive bleeding in 1 patient and hematoma in 3 patients. The average number of days in critical care was 1.2 days and 2.6 in hospitalization. Two patients required endovascular reintervention. Primary patency was present in 66.7% of the patients. DISCUSSION: The CERAB technique presents a low morbidity and mortality with an 88.9% of technical success rate. None of our patients needed Chimney CERAB procedure. Our results are similar to those reported in the literature, where they report primary patency rates between 82% and 97%.

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In this work we propose a bone metastasis model using power law growth functions in order to describe the biochemical interactions between bone cells and cancer cells. Experimental studies indicate that bone remodeling cycles are different for human life stages: childhood, young adulthood, and adulthood. In order to include such differences in our study, we estimate the model parameter values for each human life stage via bifurcation analysis. Results reveal an intrinsic relationship between the active period of remodeling cycles and the proliferation of cancer cells. Subsequently, using optimal control theory we analyze a possible antigen receptor therapy as a new treatment for bone metastasis. Theoretical results such as existence of optimal solutions are proved. Numerical simulations for late stages of bone metastasis are presented and a discussion of our results is carried out.

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BACKGROUND: In the classic descriptions of the human liver, the common hepatic duct forms at the confluence of left and right hepatic ducts. Many authors have documented variations in the intra-hepatic ductal system, but to the best of our knowledge there has been no report on bile duct variations in Caribbean populations. AIM: To evaluate the variations in bile duct anatomy using magnetic resonance cholangiography (MRC) in unselected patients at a major hepatobiliary referral centre in the Eastern Caribbean. Knowledge of the intra-hepatic biliary anatomy is important to optimize service delivery for any physician treating liver and biliary disorders. METHODS: This study was carried out at a tertiary referral hospital for hepatobiliary diseases in the Eastern Caribbean. We retrospectively evaluated magnetic resonance cholangiograms in 152 consecutive patients at this facility over a two-year period from April 1, 2017 to March 31, 2019. Two consultant radiologists experienced in MRC interpretation reviewed all scans and described biliary anatomy according to the Huang's classification. A systematic review of published studies was performed and relevant data were extracted in order to calculate the global prevalence of each biliary variant. The variants in our population were compared to the global population. RESULTS: There were 152 MRCs evaluated in this study in 86 males and 66 females. There were 109 (71.7%) persons with "classic" biliary anatomy (type A1) and variants were present in 43 (28.3%) persons. There was no statistical relationship between the presence of anatomic variants and gender or ethnicity. We encountered the following variants: 29 (19.1%) type A2, 7 (4.6%) type A3, 6 (3.95%) type A4, 0 type A5 and a single variant (quadrification) that did not fit the classification system. Compared to the global prevalence, our population had a significantly greater occurrence of A1 anatomy (71.7% vs 62.6%; P = 0.0227) and A2 trifurcations (19.1% vs 11.5%; P = 0.0069), but a significantly lower incidence of A3 variants (4.61% vs 11.5%; P = 0.0047). CONCLUSION: There are significant differences in intra-hepatic biliary anatomy in this unselected Eastern Caribbean population compared to global statistics. Specifically, persons of Caribbean descent have a greater incidence of Huang A2 trifurcations and a lower incidence of Huang A3 variants.